I think the way in which people understand immunity is very important, and perhaps the biggest problem is in thinking about our immune responses as a set process. We are at risk from numerous pathogens that have had to evolve a wide range of ways to exploit us as hosts. So as a species we have had to evolve a wide range of potential responses in order to defend ourselves, using these defences is both metabolically costly and potentially risky. They involve physical barriers, chemical barriers, alarm systems which activate a whole range of local and systemic responses etc and these responses are controlled in an attempt to be proportionate to the threat. This is important, because as the response ramps up the risks of "friendly fire" also increases, many of the symptoms we experience of disease are induced by our own immune system.
All of this means that to talk about what makes a good vaccine is difficult, this is because our immune system tends over time to develop specific responses to particular pathogens. One example of this is in the antibody response, there are very large differences in the persistence in the effectiveness of antibodies against different diseases. We know that antibody levels tend to fall quickly after infection or vaccination, but for some viruses that reproduce relatively slowly, have slow rates of mutations or in which the antibodies target conserved parts of the virus, very low levels might remain protective for a very long time and then allow the other memory cells to take over. Over time, our immune system develops very specific antibodies and the "best versions" that are preferentially produced.
This isn't the case with all viruses, RNA viruses in particular, (flu has some particular tricks in its arsenal) but the immune memory systems which develop over time, also remember the stages in the development of the best versions, so re-exposure, even to new variants, allows the innate immune system to go back in the history of how it developed the antibodies, it can target the epitopes on the new variants that haven't changed and build a new "best version" much more quickly.
So the first question has to be what do we expect a vaccine to do?, generally it is about prevention serious illness or death, some vaccines are very good at preventing disease but none can claim to be 100% effective in this, it always depends on the disease and various other factors.
Currently, the work on developing new vaccines, often against diseases that have resisted past efforts, is focussed on understanding the pathophysiology of particular infections and facilitating the development of the immune memory systems that offer the most protection. For this the best vaccines would need to target a wide range of epitopes, ideally these should be parts of the virus necessary for infection and highly conserved. This is the basis for the development of the so-called universal vaccines for coronaviruses and flu. It does seem that we need better information about the timing of vaccine schedules, the best long term responses take time to develop, and it's even possible that rapid over exposure can inhibit these responses. Generally, longer and repeated exposure allows the immune system to refine the antibodies it produces and the route of administration can affect the type of immune response, so nasal or oral vaccines using live vectors produce a greater response in the local tissues.
I think with Covid 19 we have seen all sorts of stories focussed on transmission, asymptomatic disease, reinfections and the degree of protection from infection, these have been the source of mass confusion and manipulation. I do believe that the media has had a significant role in this, but then so have politicians and many scientific bodies who have increasingly supported social control methods to enforce heath behaviours, often not based on science at all. Currently we have a situation in which the UK is basically dropping all restrictions while other countries are introducing mandatory vaccination and more social controls.
The primary purpose of the vaccines have always been to reduce the burden of serious disease, and in this they have been very effective. The current drive for booster doses has really been driven by the desire to prevent disease, which very high levels of antibodies will do, but for a short period time, it's certainly not a long term solution. Currently, we simply don't know how persistent the long term immune memory systems are and even this doesn't represent a single system, getting accurate information about this is more difficult and takes time.
So to get a good vaccine, first understand your pathogen, and how it causes disease, that's always the starting point. The question is really, how do we create a good vaccine against ... ?(insert disease here). Its worth checking out information on the development of a vaccine for HIV a hugely problematic and complex endeavour, which describes the very creative ways many of these issues are addressed.